Boolean Symbols and Expressions

As we emphasized previously, a Boolean variable can be either "true" or "false". We can use Boolean variables to represent real-life events, such as "it will rain today" or "we will go watch the soccer game today". A complex logic expression will be one that combines one or more simple Boolean variables together using "not", "and", "or", etc., relations.

Example: The statement:

It won't rain today, and we will go watch the soccer game today.

contains the two simple events "it will rain today" or "we will go watch the soccer game today". However, we first negated the 1st event (so it turned into "it won't rain today") and then ANDed it with the 2nd event.

If we denote $x = ($"$\text{it will rain today}$"$)$ and $y = ($"$\text{we will go watch the soccer game today}$"$)$, then we can represent our statement with the expression: $x'\cdot y = x'y$.